A tropical punch recipe calls for $300 \text{ ml}$ of sugar for every $2$ flavor packages. Write an equation that shows the relationship between $s$, the amount of sugar in milliliters, and $f$, the number of flavor packages for this recipe.
Solution: Let's find the constant of proportionality. In the proportional relationship between $s$, the amount of sugar in milliliters, and $f$, the number of flavor packages, one constant of proportionality is the ratio of sugar to flavor packages. It is the number we multiply by the number of flavor packages to get the amount of sugar. $f\,\times\, ?=s$ $\begin{aligned} f\,\times\, {?}&=s \\\\ {?}&=\dfrac{s}{f} \\\\ &=\dfrac{300}{2} \\\\ &={150} \end{aligned}$ The constant of proportionality is ${150}$. This means we can multiply ${150}$ by the number of flavor packages to get the amount of sugar. Now, let's write the equation: $\begin{aligned} \text{amount of sugar}&={\text{sugar to flavor package ratio}}\times\text{number of flavor packages} \\\\ s&={150}f \end{aligned}$ One correct equation is: $s = 150f$